Finite Group Databasebeta

← #26117613

Subgroups — #26117613

Order 12032.

500 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689529C212yesmaximal
2#20251456C211yesmaximal, characteristic
3C2×#15688864C212yesmaximal
4#20241269C211yesmaximal, characteristic
5C47×#1960C211yesmaximal, characteristic
6C2×#13094016C2212yes—
7#15689529—24no—
8#15689529—24no—
9C2×#13093957—22no—
10C2×#13093955—22no—
11C2×#13093935C2212yes—
12#15689063—22no—
13#15689055—22no—
14#15689053—22no—
15#15688864—24no—
16C2×C4⋊Q8×C47C2211yescharacteristic
17C2×#103×C47—22no—
18C2×#97×C47C2211yescharacteristic
19C47×#382C2211yescharacteristic
20C22×C47⋊C8—22no—
21#13094016—22no—
22#13094016—22no—
23#13094016—22no—
24#13094016—22no—
25C2×C4⋊Dic47—22no—
26C2×C4⋊Dic47D412yes—
27C2×C4⋊Dic47D412yes—
28C2×Dic47⋊C4—22no—
29C2×Dic47⋊C4—22no—
30#13093957—28no—
31#13093955—28no—
32#13093935—22no—
33#13093935D414yes—
34C47⋊#95—24no—
35C47⋊#95—22no—
36C22×Q8×C47—21no—
37C22×C8×C47—21no—
38C4⋊Q8×C47—22no—
39C4⋊Q8×C47—21no—
40C4⋊Q8×C47D412yes—
41C2×C4⋊C4×C47—22no—
42C2×C4⋊C4×C47D412yes—
43C2×C42×C47C2311yescharacteristic
44#103×C47—44no—
45#97×C47—22no—
46#95×C47—22no—
47C2×Q8×C47—22no—
48C2×Q8×C47—42no—
49C2×Q8×C47—42no—
50C2×Q8×C47—41no—
51C22×C4×C47—22no—
52C22×C4×C47—41no—
53C22×C4×C47C2×D412yes—
54C22×C4×C47C2×D411yescharacteristic
55C22×Dic47—22no—
56C22×Dic47—22no—
57C2×C8×C47—22no—
58C2×C8×C47—41no—
59C2×C8×C47—41no—
60C4⋊C4×C47—24no—
61C4⋊C4×C47—42no—
62C4⋊C4×C47—42no—
63C42×C47C2×D411yescharacteristic
64C42×C47C2×D412yes—
65C42×C47#4111yescharacteristic
66C4⋊Dic47—22no—
67C4⋊Dic47—22no—
68C4⋊Dic47—22no—
69C4⋊Dic47—22no—
70C4⋊Dic47—82no—
71Dic47⋊C4—42no—
72Dic47⋊C4—42no—
73Dic47⋊C4—42no—
74Dic47⋊C4—42no—
75C2×C47⋊C8—28no—
76C2×C47⋊C8—24no—
77C23×C47#12011yescharacteristic
78Q8×C47—44no—
79Q8×C47—82no—
80C2×C4×C47—21no—
81C2×C4×C47—21no—
82C2×C4×C47—24no—
83C2×C4×C47—42no—
84C2×C4×C47—42no—
85C2×C4×C47—44no—
86C2×C4×C47—81no—
87C2×C4×C47—81no—
88C2×C4×C47#12012yes—
89C2×C4×C47#12112yes—
90C2×C4×C47#12111yescharacteristic
91C2×C4×C47#12711yescharacteristic
92C2×Dic47—42no—
93C2×Dic47—42no—
94C2×Dic47—42no—
95C2×Dic47—42no—
96C2×Dic47—44no—
97C8×C47—42no—
98C47⋊C8—28no—
99#10087—471nomaximal, Sylow
100C22×C47#39211yescharacteristic
101C22×C47#45311yescharacteristic
102C22×C47#45411yescharacteristic
103C22×C47#45614yes—
104C4×C47—22no—
105C4×C47—22no—
106C4×C47—21no—
107C4×C47—21no—
108C4×C47—82no—
109C4×C47—82no—
110Dic47—82no—
111Dic47—82no—
112C2×#501—472no—
113#2822—471no—
114#1960D4711yescharacteristic
115C2×#330—472no—
116#1295—471no—
117C2×C47#166012yes—
118C2×C47#166312yes—
119C2×C47#200512yes—
120C2×C47#200611yescharacteristic
121C2×C4⋊Q8C2×D4711yescharacteristic
122C2×#125—472no—
123#501—944no—
124#501—944no—
125C2×#107—942no—
126C2×#106—942no—
127C2×#103—22no—
128C2×#97—472no—
129C2×#97C2×D4711yescharacteristic
130#400—942no—
131#398—942no—
132#398—942no—
133#382C2×D4711yescharacteristic
134#330—944no—
135C47#1008711yescharacteristic, complemented, Sylow
136C22×Q8—21no—
137C22×C8—21no—
138C22×C8—942no—
139C4⋊Q8—21no—
140C4⋊Q8—22no—
141C4⋊Q8D18812yes—
142#125—942no—
143#125—942no—
144#125—942no—
145#125—942no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—472no—
148C2×C4⋊C4—472no—
149C2×C4⋊C4—942no—
150C2×C4⋊C4—942no—
151C2×C4⋊C4—942no—
152C2×C4⋊C4C22⋊D4712yes—
153C2×C42C22×D4711yescharacteristic
154#107—948no—
155#106—948no—
156#103—44no—
157#97—22no—
158#97—474no—
159#97—942no—
160#95—22no—
161#95—944no—
162#95—942no—
163C2×Q8—22no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8—41no—
167C22×C4—22no—
168C22×C4—41no—
169C22×C4—942no—
170C22×C4—942no—
171C22×C4D4×D4712yes—
172C22×C4C2×C22⋊D4711yescharacteristic
173C2×C8—22no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—948no—
177C2×C8—944no—
178C4⋊C4—24no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—942no—
182C4⋊C4—942no—
183C4⋊C4—942no—
184C4⋊C4—942no—
185C4⋊C4—3762no—
186C4⋊C4—1882no—
187C4⋊C4—1882no—
188C4⋊C4—1882no—
189C4⋊C4—1882no—
190C42C2×D18811yescharacteristic
191C42#1062535011yescharacteristic
192C42D4×D4712yes—
193C23#1309399211yescharacteristic
194Q8—44no—
195Q8—82no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—24no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—44no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—1882no—
205C2×C4—1882no—
206C2×C4—1882no—
207C2×C4—1882no—
208C2×C4—1884no—
209C2×C4#1309399412yes—
210C2×C4#1309399712yes—
211C2×C4#1309399811yescharacteristic
212C2×C4#1309402011yescharacteristic
213C8—42no—
214C8—948no—
215C22#1568903211yescharacteristic
216C22#1568929011yescharacteristic
217C22#1568929511yescharacteristic
218C22#1568930414yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—82no—
225C4—3762no—
226C4—3762no—
227C2#2024269712yes—
228C2#2024271412yes—
229C2#2024442512yes—
230C2#2024442911yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1960C2
socle, prime radicalC23×C47#120
hypercenter#1960D47
hypocenterC47#10087
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
135. C47#10087semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#156895292
#202514562
C2×#156888642
#202412692
C47×#19602
#1008747